The displacement s, measured in meters for a body moving from a fixed point, P, at a time of t seconds is given by #s(t) = 10-5te^-(t/10)#. Determine the expression for the velocity v(t)?

Question

#s(t) = 10-5te^-(t/10)#
#v(t) = ?#

I'm aware that #velocity=(displacement)/(time)# and that this is worked out with differentiation, right?

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Answer 1 · 2018-04-22T21:38:41

#v(t) = -5e^(-1/10t) +1/2te^(-1/10t)#

#v(t)# is the first derivative of #s(t)# with respect to #t#.

#v(t) = (d(s(t)))/dt#

#v(t) = (d(10-5te^(-1/10t)))/dt#

The first term is 0 and we use the product rule on the second term:

#v(t) = -5e^(-1/10t) -5t(-1/10e^(-1/10t))#

#v(t) = -5e^(-1/10t) +1/2te^(-1/10t)#